Have to know height of ionosphere to desired location and whether it supports the angles. The height varies all over the globe. Very rough rule is 2000 miles per hop at HF at angles say lower than 40 degrees. Vocap will show the different hops possible. No easy answer to this.

HamCAP program from Afreet Software is an overlay that uses the VOACAP engine.

On the 'Chart" display, it will show the Elevation Angle, number of hops and the relevant ionosphere layer, e.g. "1F2" or "One Hop via F2 layer" for my selected route from Maryland to Missouri, on 20m, for a selected time and date.

HamCAP is free, and probably the best propagation tool available. I use it with the IonoProbe monitor (pay) which links with HamCAP and automatically inputs Smoothed Sunspot number (90 day) and Kilo index. IonoProbe monitor is well worth the small price.

IonoProbe and HamCAP will also interface with Afreet's DX Atlas (pay) program.

HamCAP is not well documented by Afreet, however there are several guides by others on the internet. Be aware some features are hidden, for unknown reason.

Hops vary by ionosphere layer type, E, F1,F2. From the same layer at a given height they generally tend to be the same if supported at that particular frequency. Some variations will occur versus frequency. Don't expect F layer propagation on 7 Mhz during daytime or any E layer at 14 Mhz. Also possible for more hops to be stronger than less hops at some distances.

This is a difficult topic to discuss due to the many factors and variations involved. Try reading up on some of typical and atypical propagation paths, there are many.

HamCAP program from Afreet Software is an overlay that uses the VOACAP engine.

On the 'Chart" display, it will show the Elevation Angle, number of hops and the relevant ionosphere layer, e.g. "1F2" or "One Hop via F2 layer" for my selected route from Maryland to Missouri, on 20m, for a selected time and date.

HamCAP is free, and probably the best propagation tool available. I use it with the IonoProbe monitor (pay) which links with HamCAP and automatically inputs Smoothed Sunspot number (90 day) and Kilo index. IonoProbe monitor is well worth the small price.

IonoProbe and HamCAP will also interface with Afreet's DX Atlas (pay) program.

HamCAP is not well documented by Afreet, however there are several guides by others on the internet. Be aware some features are hidden, for unknown reason.

I have a review of HamCAP, with some interesting overlays showing the HamCap prediction and what PSK reporter showed at that same time... See: http://nk7z.net/review-of-afreet-software-hamcap/ for the review. If you click the photos, they will expand.

You may already be satisfied with the answer you've gotten and KI6LZ did a nice job answering the questions. I think what KI6LZ put forth are the issues.

I want to expand the answer a bit.

To truly get the number of hops on a given path, you would need to use some sort of ray tracing software. From what I have read there are basically two varieties of ray tracing codes a 3-D code written by Jones and Stephenson and there is a 2-D approximate code written by Coleman[1993,1998]. Either of those are considered to be 'the best' in part because they numerically solve the ray paths through the ionosphere using a Hamiltonian optics formulation (or a Lagrangian approach). The issue with these methods is that they require a good knowledge of the ionosphere and a very good knowledge of Fortran to actually get them up and running.

There is a program called PropLab http://hfradio.org/swp_proplab/ which is probably the best for amateur radio operators. Unfortunately, it looks like it is pretty expensive. There is also this matlab verison (which you may be able to run on Octave - haven't tried personally) called Ionort: http://arxiv.org/ftp/arxiv/papers/1202/1202.2079.pdf I know I downloaded the source code for the latter software off of an FTP site if you look in the pdf above. I know that Ionort, at least, does solve the Jones Stephenson ray tracing code and the matlab part is basically a nice user 'front end' to the real machinery on the backside of the software.

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